196 citations · 322 across the 12 of their papers we have counts for
12 papers
DeepMartNet -- A Martingale based Deep Neural Network Learning Algorithm for Eigenvalue/BVP Problems and Optimal Stochastic Controls
Wei Cai
In this paper, we propose a neural network learning algorithm for solving eigenvalue problems and boundary value problems (BVPs) for elliptic operators and initial BVPs (IBVPs) of…
On Spectral Bias Reduction of Multi-scale Neural Networks for Regression Problems
Bo Wang, Heng Yuan, Lizuo Liu +2
In this paper, we derive diffusion equation models in the spectral domain for the evolution of training errors of two-layer multi-scale deep neural networks (MscaleDNN) \cite{caixu…
A Causality-DeepONet for Causal Responses of Linear Dynamical Systems
Lizuo Liu, Kamaljyoti Nath, Wei Cai
In this paper, we propose a DeepONet structure with causality to represent the causal linear operators between Banach spaces of time-dependent signals. The theorem of universal app…
DeepPropNet -- A Recursive Deep Propagator Neural Network for Learning Evolution PDE Operators
Lizuo Liu, Wei Cai
In this paper, we propose a deep neural network approximation to the evolution operator for time dependent PDE systems over long time period by recursively using one single neural…
Multiscale DeepONet for Nonlinear Operators in Oscillatory Function Spaces for Building Seismic Wave Responses
Lizuo Liu, Wei Cai
In this paper, we propose a multiscale DeepONet to represent nonlinear operator between Banach spaces of highly oscillatory continuous functions. The multiscale deep neural network…
FBSDE based Neural Network Algorithms for High-Dimensional Quasilinear Parabolic PDEs
Wenzhong Zhang, Wei Cai
In this paper, we propose forward and backward stochastic differential equations (FBSDEs) based deep neural network (DNN) learning algorithms for the solution of high dimensional q…